We first introduce notation specific for this paper.
For the notions not defined here, we refer the reader to [1]} and  [2]}
for the graph theory terminology and the model theory terminology, respectively.
Some of the less common general notation that we use here include the following.
The set of the first \(k\)  positive integers is denoted by \([k]\)  and \({\mathbb {N}}^*\)  denotes the set \({\mathbb {N}}\cup \lbrace \infty \rbrace \) .
If \(x\)  is a real number and \(z\)  is a positive real,
we write \(x\mod {z}\)  for the unique real \(x^{\prime }\in [0,z)\)  such that \(x=x^{\prime }+kz\)  for some \(k\in {\mathbb {Z}}\) .
Finally, if \(G\)  is a graph, then \(|G|\)  stands for the number of vertices of \(G\) .
